package com.nulldev.util.data.FastMath;

import java.util.Random;

import com.nulldev.util.VariableAPI.util.random.GlobalRandom;

public abstract class Math {

	public Math() {
	}

	/**
	 * The {@code double} value that is closer than any other to <i>e</i>, the base
	 * of the natural logarithms.
	 */
	public static final double E = 2.7182818284590452354;

	/**
	 * The {@code double} value that is closer than any other to <i>pi</i>, the
	 * ratio of the circumference of a circle to its diameter.
	 */
	public static final double PI = 3.14159265358979323846;

	/**
	 * Returns the trigonometric sine of an angle. Special cases:
	 * <ul>
	 * <li>If the argument is NaN or an infinity, then the result is NaN.
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a an angle, in radians.
	 * @return the sine of the argument.
	 */
	public static double sin(double a) {
		return java.lang.Math.sin(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the trigonometric cosine of an angle. Special cases:
	 * <ul>
	 * <li>If the argument is NaN or an infinity, then the result is NaN.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a an angle, in radians.
	 * @return the cosine of the argument.
	 */
	public static double cos(double a) {
		return java.lang.Math.cos(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the trigonometric tangent of an angle. Special cases:
	 * <ul>
	 * <li>If the argument is NaN or an infinity, then the result is NaN.
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a an angle, in radians.
	 * @return the tangent of the argument.
	 */
	public static double tan(double a) {
		return java.lang.Math.tan(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the arc sine of a value; the returned angle is in the range
	 * -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
	 * <ul>
	 * <li>If the argument is NaN or its absolute value is greater than 1, then the
	 * result is NaN.
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a the value whose arc sine is to be returned.
	 * @return the arc sine of the argument.
	 */
	public static double asin(double a) {
		return java.lang.Math.asin(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the arc cosine of a value; the returned angle is in the range 0.0
	 * through <i>pi</i>. Special case:
	 * <ul>
	 * <li>If the argument is NaN or its absolute value is greater than 1, then the
	 * result is NaN.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a the value whose arc cosine is to be returned.
	 * @return the arc cosine of the argument.
	 */
	public static double acos(double a) {
		return java.lang.Math.acos(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the arc tangent of a value; the returned angle is in the range
	 * -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
	 * <ul>
	 * <li>If the argument is NaN, then the result is NaN.
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a the value whose arc tangent is to be returned.
	 * @return the arc tangent of the argument.
	 */
	public static double atan(double a) {
		return java.lang.Math.atan(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Converts an angle measured in degrees to an approximately equivalent angle
	 * measured in radians. The conversion from degrees to radians is generally
	 * inexact.
	 *
	 * @param angdeg an angle, in degrees
	 * @return the measurement of the angle {@code angdeg} in radians.
	 * @since 1.2
	 */
	public static double toRadians(double angdeg) {
		return angdeg / 180.0 * PI;
	}

	/**
	 * Converts an angle measured in radians to an approximately equivalent angle
	 * measured in degrees. The conversion from radians to degrees is generally
	 * inexact; users should <i>not</i> expect {@code cos(toRadians(90.0))} to
	 * exactly equal {@code 0.0}.
	 *
	 * @param angrad an angle, in radians
	 * @return the measurement of the angle {@code angrad} in degrees.
	 * @since 1.2
	 */
	public static double toDegrees(double angrad) {
		return angrad * 180.0 / PI;
	}

	/**
	 * Returns Euler's number <i>e</i> raised to the power of a {@code double}
	 * value. Special cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is NaN.
	 * <li>If the argument is positive infinity, then the result is positive
	 * infinity.
	 * <li>If the argument is negative infinity, then the result is positive zero.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a the exponent to raise <i>e</i> to.
	 * @return the value <i>e</i><sup>{@code a}</sup>, where <i>e</i> is the base of
	 *         the natural logarithms.
	 */
	public static double exp(double a) {
		return java.lang.Math.exp(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the natural logarithm (base <i>e</i>) of a {@code double} value.
	 * Special cases:
	 * <ul>
	 * <li>If the argument is NaN or less than zero, then the result is NaN.
	 * <li>If the argument is positive infinity, then the result is positive
	 * infinity.
	 * <li>If the argument is positive zero or negative zero, then the result is
	 * negative infinity.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a a value
	 * @return the value ln&nbsp;{@code a}, the natural logarithm of {@code a}.
	 */
	public static double log(double a) {
		return java.lang.Math.log(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the base 10 logarithm of a {@code double} value. Special cases:
	 *
	 * <ul>
	 * <li>If the argument is NaN or less than zero, then the result is NaN.
	 * <li>If the argument is positive infinity, then the result is positive
	 * infinity.
	 * <li>If the argument is positive zero or negative zero, then the result is
	 * negative infinity.
	 * <li>If the argument is equal to 10<sup><i>n</i></sup> for integer <i>n</i>,
	 * then the result is <i>n</i>.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a a value
	 * @return the base 10 logarithm of {@code a}.
	 * @since 1.5
	 */
	public static double log10(double a) {
		return java.lang.Math.log10(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the correctly rounded positive square root of a {@code double} value.
	 * Special cases:
	 * <ul>
	 * <li>If the argument is NaN or less than zero, then the result is NaN.
	 * <li>If the argument is positive infinity, then the result is positive
	 * infinity.
	 * <li>If the argument is positive zero or negative zero, then the result is the
	 * same as the argument.
	 * </ul>
	 * Otherwise, the result is the {@code double} value closest to the true
	 * mathematical square root of the argument value.
	 *
	 * @param a a value.
	 * @return the positive square root of {@code a}. If the argument is NaN or less
	 *         than zero, the result is NaN.
	 */
	public static double sqrt(double a) {
		return java.lang.Math.sqrt(a); // default impl. delegates to java.lang.Math
		// Note that hardware sqrt instructions
		// frequently can be directly used by JITs
		// and should be much faster than doing
		// Math.sqrt in software.
	}

	/**
	 * Returns the cube root of a {@code double} value. For positive finite
	 * {@code x}, {@code cbrt(-x) ==
	 * -cbrt(x)}; that is, the cube root of a negative value is the negative of the
	 * cube root of that value's magnitude.
	 *
	 * Special cases:
	 *
	 * <ul>
	 *
	 * <li>If the argument is NaN, then the result is NaN.
	 *
	 * <li>If the argument is infinite, then the result is an infinity with the same
	 * sign as the argument.
	 *
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result.
	 *
	 * @param a a value.
	 * @return the cube root of {@code a}.
	 * @since 1.5
	 */
	public static double cbrt(double a) {
		return java.lang.Math.cbrt(a);
	}

	/**
	 * Computes the remainder operation on two arguments as prescribed by the IEEE
	 * 754 standard. The remainder value is mathematically equal to
	 * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>, where <i>n</i> is
	 * the mathematical integer closest to the exact mathematical value of the
	 * quotient {@code f1/f2}, and if two mathematical integers are equally close to
	 * {@code f1/f2}, then <i>n</i> is the integer that is even. If the remainder is
	 * zero, its sign is the same as the sign of the first argument. Special cases:
	 * <ul>
	 * <li>If either argument is NaN, or the first argument is infinite, or the
	 * second argument is positive zero or negative zero, then the result is NaN.
	 * <li>If the first argument is finite and the second argument is infinite, then
	 * the result is the same as the first argument.
	 * </ul>
	 *
	 * @param f1 the dividend.
	 * @param f2 the divisor.
	 * @return the remainder when {@code f1} is divided by {@code f2}.
	 */
	public static double IEEEremainder(double f1, double f2) {
		return java.lang.Math.IEEEremainder(f1, f2); // delegate to java.lang.Math
	}

	/**
	 * Returns the smallest (closest to negative infinity) {@code double} value that
	 * is greater than or equal to the argument and is equal to a mathematical
	 * integer. Special cases:
	 * <ul>
	 * <li>If the argument value is already equal to a mathematical integer, then
	 * the result is the same as the argument.
	 * <li>If the argument is NaN or an infinity or positive zero or negative zero,
	 * then the result is the same as the argument.
	 * <li>If the argument value is less than zero but greater than -1.0, then the
	 * result is negative zero.
	 * </ul>
	 * Note that the value of {@code Math.ceil(x)} is exactly the value of
	 * {@code -Math.floor(-x)}.
	 *
	 *
	 * @param a a value.
	 * @return the smallest (closest to negative infinity) floating-point value that
	 *         is greater than or equal to the argument and is equal to a
	 *         mathematical integer.
	 */
	public static double ceil(double a) {
		return java.lang.Math.ceil(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the largest (closest to positive infinity) {@code double} value that
	 * is less than or equal to the argument and is equal to a mathematical integer.
	 * Special cases:
	 * <ul>
	 * <li>If the argument value is already equal to a mathematical integer, then
	 * the result is the same as the argument.
	 * <li>If the argument is NaN or an infinity or positive zero or negative zero,
	 * then the result is the same as the argument.
	 * </ul>
	 *
	 * @param a a value.
	 * @return the largest (closest to positive infinity) floating-point value that
	 *         less than or equal to the argument and is equal to a mathematical
	 *         integer.
	 */
	public static double floor(double a) {
		return java.lang.Math.floor(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the {@code double} value that is closest in value to the argument and
	 * is equal to a mathematical integer. If two {@code double} values that are
	 * mathematical integers are equally close, the result is the integer value that
	 * is even. Special cases:
	 * <ul>
	 * <li>If the argument value is already equal to a mathematical integer, then
	 * the result is the same as the argument.
	 * <li>If the argument is NaN or an infinity or positive zero or negative zero,
	 * then the result is the same as the argument.
	 * </ul>
	 *
	 * @param a a {@code double} value.
	 * @return the closest floating-point value to {@code a} that is equal to a
	 *         mathematical integer.
	 */
	public static double rint(double a) {
		return java.lang.Math.rint(a); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the angle <i>theta</i> from the conversion of rectangular coordinates
	 * ({@code x},&nbsp;{@code y}) to polar coordinates (r,&nbsp;<i>theta</i>). This
	 * method computes the phase <i>theta</i> by computing an arc tangent of
	 * {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special cases:
	 * <ul>
	 * <li>If either argument is NaN, then the result is NaN.
	 * <li>If the first argument is positive zero and the second argument is
	 * positive, or the first argument is positive and finite and the second
	 * argument is positive infinity, then the result is positive zero.
	 * <li>If the first argument is negative zero and the second argument is
	 * positive, or the first argument is negative and finite and the second
	 * argument is positive infinity, then the result is negative zero.
	 * <li>If the first argument is positive zero and the second argument is
	 * negative, or the first argument is positive and finite and the second
	 * argument is negative infinity, then the result is the {@code double} value
	 * closest to <i>pi</i>.
	 * <li>If the first argument is negative zero and the second argument is
	 * negative, or the first argument is negative and finite and the second
	 * argument is negative infinity, then the result is the {@code double} value
	 * closest to -<i>pi</i>.
	 * <li>If the first argument is positive and the second argument is positive
	 * zero or negative zero, or the first argument is positive infinity and the
	 * second argument is finite, then the result is the {@code double} value
	 * closest to <i>pi</i>/2.
	 * <li>If the first argument is negative and the second argument is positive
	 * zero or negative zero, or the first argument is negative infinity and the
	 * second argument is finite, then the result is the {@code double} value
	 * closest to -<i>pi</i>/2.
	 * <li>If both arguments are positive infinity, then the result is the
	 * {@code double} value closest to <i>pi</i>/4.
	 * <li>If the first argument is positive infinity and the second argument is
	 * negative infinity, then the result is the {@code double} value closest to
	 * 3*<i>pi</i>/4.
	 * <li>If the first argument is negative infinity and the second argument is
	 * positive infinity, then the result is the {@code double} value closest to
	 * -<i>pi</i>/4.
	 * <li>If both arguments are negative infinity, then the result is the
	 * {@code double} value closest to -3*<i>pi</i>/4.
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 2 ulps of the exact result. Results must
	 * be semi-monotonic.
	 *
	 * @param y the ordinate coordinate
	 * @param x the abscissa coordinate
	 * @return the <i>theta</i> component of the point (<i>r</i>,&nbsp;<i>theta</i>)
	 *         in polar coordinates that corresponds to the point
	 *         (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
	 */
	public static double atan2(double y, double x) {
		return java.lang.Math.atan2(y, x); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the value of the first argument raised to the power of the second
	 * argument. Special cases:
	 *
	 * <ul>
	 * <li>If the second argument is positive or negative zero, then the result is
	 * 1.0.
	 * <li>If the second argument is 1.0, then the result is the same as the first
	 * argument.
	 * <li>If the second argument is NaN, then the result is NaN.
	 * <li>If the first argument is NaN and the second argument is nonzero, then the
	 * result is NaN.
	 *
	 * <li>If
	 * <ul>
	 * <li>the absolute value of the first argument is greater than 1 and the second
	 * argument is positive infinity, or
	 * <li>the absolute value of the first argument is less than 1 and the second
	 * argument is negative infinity,
	 * </ul>
	 * then the result is positive infinity.
	 *
	 * <li>If
	 * <ul>
	 * <li>the absolute value of the first argument is greater than 1 and the second
	 * argument is negative infinity, or
	 * <li>the absolute value of the first argument is less than 1 and the second
	 * argument is positive infinity,
	 * </ul>
	 * then the result is positive zero.
	 *
	 * <li>If the absolute value of the first argument equals 1 and the second
	 * argument is infinite, then the result is NaN.
	 *
	 * <li>If
	 * <ul>
	 * <li>the first argument is positive zero and the second argument is greater
	 * than zero, or
	 * <li>the first argument is positive infinity and the second argument is less
	 * than zero,
	 * </ul>
	 * then the result is positive zero.
	 *
	 * <li>If
	 * <ul>
	 * <li>the first argument is positive zero and the second argument is less than
	 * zero, or
	 * <li>the first argument is positive infinity and the second argument is
	 * greater than zero,
	 * </ul>
	 * then the result is positive infinity.
	 *
	 * <li>If
	 * <ul>
	 * <li>the first argument is negative zero and the second argument is greater
	 * than zero but not a finite odd integer, or
	 * <li>the first argument is negative infinity and the second argument is less
	 * than zero but not a finite odd integer,
	 * </ul>
	 * then the result is positive zero.
	 *
	 * <li>If
	 * <ul>
	 * <li>the first argument is negative zero and the second argument is a positive
	 * finite odd integer, or
	 * <li>the first argument is negative infinity and the second argument is a
	 * negative finite odd integer,
	 * </ul>
	 * then the result is negative zero.
	 *
	 * <li>If
	 * <ul>
	 * <li>the first argument is negative zero and the second argument is less than
	 * zero but not a finite odd integer, or
	 * <li>the first argument is negative infinity and the second argument is
	 * greater than zero but not a finite odd integer,
	 * </ul>
	 * then the result is positive infinity.
	 *
	 * <li>If
	 * <ul>
	 * <li>the first argument is negative zero and the second argument is a negative
	 * finite odd integer, or
	 * <li>the first argument is negative infinity and the second argument is a
	 * positive finite odd integer,
	 * </ul>
	 * then the result is negative infinity.
	 *
	 * <li>If the first argument is finite and less than zero
	 * <ul>
	 * <li>if the second argument is a finite even integer, the result is equal to
	 * the result of raising the absolute value of the first argument to the power
	 * of the second argument
	 *
	 * <li>if the second argument is a finite odd integer, the result is equal to
	 * the negative of the result of raising the absolute value of the first
	 * argument to the power of the second argument
	 *
	 * <li>if the second argument is finite and not an integer, then the result is
	 * NaN.
	 * </ul>
	 *
	 * <li>If both arguments are integers, then the result is exactly equal to the
	 * mathematical result of raising the first argument to the power of the second
	 * argument if that result can in fact be represented exactly as a
	 * {@code double} value.
	 * </ul>
	 *
	 * <p>
	 * (In the foregoing descriptions, a floating-point value is considered to be an
	 * integer if and only if it is finite and a fixed point of the method
	 * {@link #ceil ceil} or, equivalently, a fixed point of the method
	 * {@link #floor floor}. A value is a fixed point of a one-argument method if
	 * and only if the result of applying the method to the value is equal to the
	 * value.)
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param a the base.
	 * @param b the exponent.
	 * @return the value {@code a}<sup>{@code b}</sup>.
	 */
	public static double pow(double a, double b) {
		return java.lang.Math.pow(a, b); // default impl. delegates to java.lang.Math
	}

	/**
	 * Returns the closest {@code int} to the argument, with ties rounding to
	 * positive infinity.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is 0.
	 * <li>If the argument is negative infinity or any value less than or equal to
	 * the value of {@code Integer.MIN_VALUE}, the result is equal to the value of
	 * {@code Integer.MIN_VALUE}.
	 * <li>If the argument is positive infinity or any value greater than or equal
	 * to the value of {@code Integer.MAX_VALUE}, the result is equal to the value
	 * of {@code Integer.MAX_VALUE}.
	 * </ul>
	 *
	 * @param a a floating-point value to be rounded to an integer.
	 * @return the value of the argument rounded to the nearest {@code int} value.
	 * @see java.lang.Integer#MAX_VALUE
	 * @see java.lang.Integer#MIN_VALUE
	 */
	public static int round(float a) {
		return java.lang.Math.round(a);
	}

	/**
	 * Returns the closest {@code long} to the argument, with ties rounding to
	 * positive infinity.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is 0.
	 * <li>If the argument is negative infinity or any value less than or equal to
	 * the value of {@code Long.MIN_VALUE}, the result is equal to the value of
	 * {@code Long.MIN_VALUE}.
	 * <li>If the argument is positive infinity or any value greater than or equal
	 * to the value of {@code Long.MAX_VALUE}, the result is equal to the value of
	 * {@code Long.MAX_VALUE}.
	 * </ul>
	 *
	 * @param a a floating-point value to be rounded to a {@code long}.
	 * @return the value of the argument rounded to the nearest {@code long} value.
	 * @see java.lang.Long#MAX_VALUE
	 * @see java.lang.Long#MIN_VALUE
	 */
	public static long round(double a) {
		return java.lang.Math.round(a);
	}

	private static final class RandomNumberGeneratorHolder {
		static final Random randomNumberGenerator = GlobalRandom.getGlobalInsecureRandom();
	}

	/**
	 * Returns a {@code double} value with a positive sign, greater than or equal to
	 * {@code 0.0} and less than {@code 1.0}. Returned values are chosen
	 * pseudorandomly with (approximately) uniform distribution from that range.
	 *
	 * <p>
	 * When this method is first called, it creates a single new pseudorandom-number
	 * generator, exactly as if by the expression
	 *
	 * <blockquote>{@code new java.util.Random()}</blockquote>
	 *
	 * This new pseudorandom-number generator is used thereafter for all calls to
	 * this method and is used nowhere else.
	 *
	 * <p>
	 * This method is properly synchronized to allow correct use by more than one
	 * thread. However, if many threads need to generate pseudorandom numbers at a
	 * great rate, it may reduce contention for each thread to have its own
	 * pseudorandom-number generator.
	 *
	 * @return a pseudorandom {@code double} greater than or equal to {@code 0.0}
	 *         and less than {@code 1.0}.
	 * @see Random#nextDouble()
	 */
	public static double random() {
		return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
	}

	/**
	 * Returns the sum of its arguments, throwing an exception if the result
	 * overflows an {@code int}.
	 *
	 * @param x the first value
	 * @param y the second value
	 * @return the result
	 * @throws ArithmeticException if the result overflows an int
	 * @since 1.8
	 */
	public static int addExact(int x, int y) {
		int r = x + y;
		// HD 2-12 Overflow iff both arguments have the opposite sign of the result
		if (((x ^ r) & (y ^ r)) < 0) {
			throw new ArithmeticException("integer overflow");
		}
		return r;
	}

	/**
	 * Returns the sum of its arguments, throwing an exception if the result
	 * overflows a {@code long}.
	 *
	 * @param x the first value
	 * @param y the second value
	 * @return the result
	 * @throws ArithmeticException if the result overflows a long
	 * @since 1.8
	 */
	public static long addExact(long x, long y) {
		long r = x + y;
		// HD 2-12 Overflow iff both arguments have the opposite sign of the result
		if (((x ^ r) & (y ^ r)) < 0) {
			throw new ArithmeticException("long overflow");
		}
		return r;
	}

	/**
	 * Returns the difference of the arguments, throwing an exception if the result
	 * overflows an {@code int}.
	 *
	 * @param x the first value
	 * @param y the second value to subtract from the first
	 * @return the result
	 * @throws ArithmeticException if the result overflows an int
	 * @since 1.8
	 */
	public static int subtractExact(int x, int y) {
		int r = x - y;
		// HD 2-12 Overflow iff the arguments have different signs and
		// the sign of the result is different than the sign of x
		if (((x ^ y) & (x ^ r)) < 0) {
			throw new ArithmeticException("integer overflow");
		}
		return r;
	}

	/**
	 * Returns the difference of the arguments, throwing an exception if the result
	 * overflows a {@code long}.
	 *
	 * @param x the first value
	 * @param y the second value to subtract from the first
	 * @return the result
	 * @throws ArithmeticException if the result overflows a long
	 * @since 1.8
	 */
	public static long subtractExact(long x, long y) {
		long r = x - y;
		// HD 2-12 Overflow iff the arguments have different signs and
		// the sign of the result is different than the sign of x
		if (((x ^ y) & (x ^ r)) < 0) {
			throw new ArithmeticException("long overflow");
		}
		return r;
	}

	/**
	 * Returns the product of the arguments, throwing an exception if the result
	 * overflows an {@code int}.
	 *
	 * @param x the first value
	 * @param y the second value
	 * @return the result
	 * @throws ArithmeticException if the result overflows an int
	 * @since 1.8
	 */
	public static int multiplyExact(int x, int y) {
		long r = (long) x * (long) y;
		if ((int) r != r) {
			throw new ArithmeticException("integer overflow");
		}
		return (int) r;
	}

	/**
	 * Returns the product of the arguments, throwing an exception if the result
	 * overflows a {@code long}.
	 *
	 * @param x the first value
	 * @param y the second value
	 * @return the result
	 * @throws ArithmeticException if the result overflows a long
	 * @since 1.8
	 */
	public static long multiplyExact(long x, long y) {
		long r = x * y;
		long ax = Math.abs(x);
		long ay = Math.abs(y);
		if (((ax | ay) >>> 31 != 0)) {
			// Some bits greater than 2^31 that might cause overflow
			// Check the result using the divide operator
			// and check for the special case of Long.MIN_VALUE * -1
			if (((y != 0) && (r / y != x)) || (x == Long.MIN_VALUE && y == -1)) {
				throw new ArithmeticException("long overflow");
			}
		}
		return r;
	}

	/**
	 * Returns the argument incremented by one, throwing an exception if the result
	 * overflows an {@code int}.
	 *
	 * @param a the value to increment
	 * @return the result
	 * @throws ArithmeticException if the result overflows an int
	 * @since 1.8
	 */
	public static int incrementExact(int a) {
		if (a == Integer.MAX_VALUE) {
			throw new ArithmeticException("integer overflow");
		}

		return a + 1;
	}

	/**
	 * Returns the argument incremented by one, throwing an exception if the result
	 * overflows a {@code long}.
	 *
	 * @param a the value to increment
	 * @return the result
	 * @throws ArithmeticException if the result overflows a long
	 * @since 1.8
	 */
	public static long incrementExact(long a) {
		if (a == Long.MAX_VALUE) {
			throw new ArithmeticException("long overflow");
		}

		return a + 1L;
	}

	/**
	 * Returns the argument decremented by one, throwing an exception if the result
	 * overflows an {@code int}.
	 *
	 * @param a the value to decrement
	 * @return the result
	 * @throws ArithmeticException if the result overflows an int
	 * @since 1.8
	 */
	public static int decrementExact(int a) {
		if (a == Integer.MIN_VALUE) {
			throw new ArithmeticException("integer overflow");
		}

		return a - 1;
	}

	/**
	 * Returns the argument decremented by one, throwing an exception if the result
	 * overflows a {@code long}.
	 *
	 * @param a the value to decrement
	 * @return the result
	 * @throws ArithmeticException if the result overflows a long
	 * @since 1.8
	 */
	public static long decrementExact(long a) {
		if (a == Long.MIN_VALUE) {
			throw new ArithmeticException("long overflow");
		}

		return a - 1L;
	}

	/**
	 * Returns the negation of the argument, throwing an exception if the result
	 * overflows an {@code int}.
	 *
	 * @param a the value to negate
	 * @return the result
	 * @throws ArithmeticException if the result overflows an int
	 * @since 1.8
	 */
	public static int negateExact(int a) {
		if (a == Integer.MIN_VALUE) {
			throw new ArithmeticException("integer overflow");
		}

		return -a;
	}

	/**
	 * Returns the negation of the argument, throwing an exception if the result
	 * overflows a {@code long}.
	 *
	 * @param a the value to negate
	 * @return the result
	 * @throws ArithmeticException if the result overflows a long
	 * @since 1.8
	 */
	public static long negateExact(long a) {
		if (a == Long.MIN_VALUE) {
			throw new ArithmeticException("long overflow");
		}

		return -a;
	}

	/**
	 * Returns the value of the {@code long} argument; throwing an exception if the
	 * value overflows an {@code int}.
	 *
	 * @param value the long value
	 * @return the argument as an int
	 * @throws ArithmeticException if the {@code argument} overflows an int
	 * @since 1.8
	 */
	public static int toIntExact(long value) {
		if ((int) value != value) {
			throw new ArithmeticException("integer overflow");
		}
		return (int) value;
	}

	/**
	 * Returns the largest (closest to positive infinity) {@code int} value that is
	 * less than or equal to the algebraic quotient. There is one special case, if
	 * the dividend is the {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the
	 * divisor is {@code -1}, then integer overflow occurs and the result is equal
	 * to the {@code Integer.MIN_VALUE}.
	 * <p>
	 * Normal integer division operates under the round to zero rounding mode
	 * (truncation). This operation instead acts under the round toward negative
	 * infinity (floor) rounding mode. The floor rounding mode gives different
	 * results than truncation when the exact result is negative.
	 * <ul>
	 * <li>If the signs of the arguments are the same, the results of
	 * {@code floorDiv} and the {@code /} operator are the same. <br>
	 * For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
	 * <li>If the signs of the arguments are different, the quotient is negative and
	 * {@code floorDiv} returns the integer less than or equal to the quotient and
	 * the {@code /} operator returns the integer closest to zero.<br>
	 * For example, {@code floorDiv(-4, 3) == -2}, whereas {@code (-4 / 3) == -1}.
	 * </li>
	 * </ul>
	 * <p>
	 *
	 * @param x the dividend
	 * @param y the divisor
	 * @return the largest (closest to positive infinity) {@code int} value that is
	 *         less than or equal to the algebraic quotient.
	 * @throws ArithmeticException if the divisor {@code y} is zero
	 * @see #floorMod(int, int)
	 * @see #floor(double)
	 * @since 1.8
	 */
	public static int floorDiv(int x, int y) {
		int r = x / y;
		// if the signs are different and modulo not zero, round down
		if ((x ^ y) < 0 && (r * y != x)) {
			r--;
		}
		return r;
	}

	/**
	 * Returns the largest (closest to positive infinity) {@code long} value that is
	 * less than or equal to the algebraic quotient. There is one special case, if
	 * the dividend is the {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the
	 * divisor is {@code -1}, then integer overflow occurs and the result is equal
	 * to the {@code Long.MIN_VALUE}.
	 * <p>
	 * Normal integer division operates under the round to zero rounding mode
	 * (truncation). This operation instead acts under the round toward negative
	 * infinity (floor) rounding mode. The floor rounding mode gives different
	 * results than truncation when the exact result is negative.
	 * <p>
	 * For examples, see {@link #floorDiv(int, int)}.
	 *
	 * @param x the dividend
	 * @param y the divisor
	 * @return the largest (closest to positive infinity) {@code long} value that is
	 *         less than or equal to the algebraic quotient.
	 * @throws ArithmeticException if the divisor {@code y} is zero
	 * @see #floorMod(long, long)
	 * @see #floor(double)
	 * @since 1.8
	 */
	public static long floorDiv(long x, long y) {
		long r = x / y;
		// if the signs are different and modulo not zero, round down
		if ((x ^ y) < 0 && (r * y != x)) {
			r--;
		}
		return r;
	}

	/**
	 * Returns the floor modulus of the {@code int} arguments.
	 * <p>
	 * The floor modulus is {@code x - (floorDiv(x, y) * y)}, has the same sign as
	 * the divisor {@code y}, and is in the range of {@code -abs(y) < r < +abs(y)}.
	 *
	 * <p>
	 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
	 * <ul>
	 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
	 * </ul>
	 * <p>
	 * The difference in values between {@code floorMod} and the {@code %} operator
	 * is due to the difference between {@code floorDiv} that returns the integer
	 * less than or equal to the quotient and the {@code /} operator that returns
	 * the integer closest to zero.
	 * <p>
	 * Examples:
	 * <ul>
	 * <li>If the signs of the arguments are the same, the results of
	 * {@code floorMod} and the {@code %} operator are the same. <br>
	 * <ul>
	 * <li>{@code floorMod(4, 3) == 1}; &nbsp; and {@code (4 % 3) == 1}</li>
	 * </ul>
	 * <li>If the signs of the arguments are different, the results differ from the
	 * {@code %} operator.<br>
	 * <ul>
	 * <li>{@code floorMod(+4, -3) == -2}; &nbsp; and {@code (+4 % -3) == +1}</li>
	 * <li>{@code floorMod(-4, +3) == +2}; &nbsp; and {@code (-4 % +3) == -1}</li>
	 * <li>{@code floorMod(-4, -3) == -1}; &nbsp; and {@code (-4 % -3) == -1 }</li>
	 * </ul>
	 * </li>
	 * </ul>
	 * <p>
	 * If the signs of arguments are unknown and a positive modulus is needed it can
	 * be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
	 *
	 * @param x the dividend
	 * @param y the divisor
	 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
	 * @throws ArithmeticException if the divisor {@code y} is zero
	 * @see #floorDiv(int, int)
	 * @since 1.8
	 */
	public static int floorMod(int x, int y) {
		int r = x - floorDiv(x, y) * y;
		return r;
	}

	/**
	 * Returns the floor modulus of the {@code long} arguments.
	 * <p>
	 * The floor modulus is {@code x - (floorDiv(x, y) * y)}, has the same sign as
	 * the divisor {@code y}, and is in the range of {@code -abs(y) < r < +abs(y)}.
	 *
	 * <p>
	 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
	 * <ul>
	 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
	 * </ul>
	 * <p>
	 * For examples, see {@link #floorMod(int, int)}.
	 *
	 * @param x the dividend
	 * @param y the divisor
	 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
	 * @throws ArithmeticException if the divisor {@code y} is zero
	 * @see #floorDiv(long, long)
	 * @since 1.8
	 */
	public static long floorMod(long x, long y) {
		return x - floorDiv(x, y) * y;
	}

	/**
	 * Returns the absolute value of an {@code int} value. If the argument is not
	 * negative, the argument is returned. If the argument is negative, the negation
	 * of the argument is returned.
	 *
	 * <p>
	 * Note that if the argument is equal to the value of {@link Integer#MIN_VALUE},
	 * the most negative representable {@code int} value, the result is that same
	 * value, which is negative.
	 *
	 * @param a the argument whose absolute value is to be determined
	 * @return the absolute value of the argument.
	 */
	public static int abs(int a) {
		return (a < 0) ? -a : a;
	}

	/**
	 * Returns the absolute value of a {@code long} value. If the argument is not
	 * negative, the argument is returned. If the argument is negative, the negation
	 * of the argument is returned.
	 *
	 * <p>
	 * Note that if the argument is equal to the value of {@link Long#MIN_VALUE},
	 * the most negative representable {@code long} value, the result is that same
	 * value, which is negative.
	 *
	 * @param a the argument whose absolute value is to be determined
	 * @return the absolute value of the argument.
	 */
	public static long abs(long a) {
		return (a < 0) ? -a : a;
	}

	/**
	 * Returns the absolute value of a {@code float} value. If the argument is not
	 * negative, the argument is returned. If the argument is negative, the negation
	 * of the argument is returned. Special cases:
	 * <ul>
	 * <li>If the argument is positive zero or negative zero, the result is positive
	 * zero.
	 * <li>If the argument is infinite, the result is positive infinity.
	 * <li>If the argument is NaN, the result is NaN.
	 * </ul>
	 * In other words, the result is the same as the value of the expression:
	 * <p>
	 * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
	 *
	 * @param a the argument whose absolute value is to be determined
	 * @return the absolute value of the argument.
	 */
	public static float abs(float a) {
		return (a <= 0.0F) ? 0.0F - a : a;
	}

	/**
	 * Returns the absolute value of a {@code double} value. If the argument is not
	 * negative, the argument is returned. If the argument is negative, the negation
	 * of the argument is returned. Special cases:
	 * <ul>
	 * <li>If the argument is positive zero or negative zero, the result is positive
	 * zero.
	 * <li>If the argument is infinite, the result is positive infinity.
	 * <li>If the argument is NaN, the result is NaN.
	 * </ul>
	 * In other words, the result is the same as the value of the expression:
	 * <p>
	 * {@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
	 *
	 * @param a the argument whose absolute value is to be determined
	 * @return the absolute value of the argument.
	 */
	public static double abs(double a) {
		return (a <= 0.0D) ? 0.0D - a : a;
	}

	/**
	 * Returns the greater of two {@code int} values. That is, the result is the
	 * argument closer to the value of {@link Integer#MAX_VALUE}. If the arguments
	 * have the same value, the result is that same value.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the larger of {@code a} and {@code b}.
	 */
	public static int max(int a, int b) {
		return (a >= b) ? a : b;
	}

	/**
	 * Returns the greater of two {@code long} values. That is, the result is the
	 * argument closer to the value of {@link Long#MAX_VALUE}. If the arguments have
	 * the same value, the result is that same value.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the larger of {@code a} and {@code b}.
	 */
	public static long max(long a, long b) {
		return (a >= b) ? a : b;
	}

	// Use raw bit-wise conversions on guaranteed non-NaN arguments.
	private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
	private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);

	/**
	 * Returns the greater of two {@code float} values. That is, the result is the
	 * argument closer to positive infinity. If the arguments have the same value,
	 * the result is that same value. If either value is NaN, then the result is
	 * NaN. Unlike the numerical comparison operators, this method considers
	 * negative zero to be strictly smaller than positive zero. If one argument is
	 * positive zero and the other negative zero, the result is positive zero.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the larger of {@code a} and {@code b}.
	 */
	public static float max(float a, float b) {
		if (a != a)
			return a; // a is NaN
		if ((a == 0.0f) && (b == 0.0f) && (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
			// Raw conversion ok since NaN can't map to -0.0.
			return b;
		}
		return (a >= b) ? a : b;
	}

	/**
	 * Returns the greater of two {@code double} values. That is, the result is the
	 * argument closer to positive infinity. If the arguments have the same value,
	 * the result is that same value. If either value is NaN, then the result is
	 * NaN. Unlike the numerical comparison operators, this method considers
	 * negative zero to be strictly smaller than positive zero. If one argument is
	 * positive zero and the other negative zero, the result is positive zero.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the larger of {@code a} and {@code b}.
	 */
	public static double max(double a, double b) {
		if (a != a)
			return a; // a is NaN
		if ((a == 0.0d) && (b == 0.0d) && (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
			// Raw conversion ok since NaN can't map to -0.0.
			return b;
		}
		return (a >= b) ? a : b;
	}

	/**
	 * Returns the smaller of two {@code int} values. That is, the result the
	 * argument closer to the value of {@link Integer#MIN_VALUE}. If the arguments
	 * have the same value, the result is that same value.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the smaller of {@code a} and {@code b}.
	 */
	public static int min(int a, int b) {
		return (a <= b) ? a : b;
	}

	/**
	 * Returns the smaller of two {@code long} values. That is, the result is the
	 * argument closer to the value of {@link Long#MIN_VALUE}. If the arguments have
	 * the same value, the result is that same value.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the smaller of {@code a} and {@code b}.
	 */
	public static long min(long a, long b) {
		return (a <= b) ? a : b;
	}

	/**
	 * Returns the smaller of two {@code float} values. That is, the result is the
	 * value closer to negative infinity. If the arguments have the same value, the
	 * result is that same value. If either value is NaN, then the result is NaN.
	 * Unlike the numerical comparison operators, this method considers negative
	 * zero to be strictly smaller than positive zero. If one argument is positive
	 * zero and the other is negative zero, the result is negative zero.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the smaller of {@code a} and {@code b}.
	 */
	public static float min(float a, float b) {
		if (a != a)
			return a; // a is NaN
		if ((a == 0.0f) && (b == 0.0f) && (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
			// Raw conversion ok since NaN can't map to -0.0.
			return b;
		}
		return (a <= b) ? a : b;
	}

	/**
	 * Returns the smaller of two {@code double} values. That is, the result is the
	 * value closer to negative infinity. If the arguments have the same value, the
	 * result is that same value. If either value is NaN, then the result is NaN.
	 * Unlike the numerical comparison operators, this method considers negative
	 * zero to be strictly smaller than positive zero. If one argument is positive
	 * zero and the other is negative zero, the result is negative zero.
	 *
	 * @param a an argument.
	 * @param b another argument.
	 * @return the smaller of {@code a} and {@code b}.
	 */
	public static double min(double a, double b) {
		if (a != a)
			return a; // a is NaN
		if ((a == 0.0d) && (b == 0.0d) && (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
			// Raw conversion ok since NaN can't map to -0.0.
			return b;
		}
		return (a <= b) ? a : b;
	}

	/**
	 * Returns the size of an ulp of the argument. An ulp, unit in the last place,
	 * of a {@code double} value is the positive distance between this
	 * floating-point value and the {@code
	 * double} value next larger in magnitude. Note that for non-NaN <i>x</i>,
	 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, then the result is NaN.
	 * <li>If the argument is positive or negative infinity, then the result is
	 * positive infinity.
	 * <li>If the argument is positive or negative zero, then the result is
	 * {@code Double.MIN_VALUE}.
	 * <li>If the argument is &plusmn;{@code Double.MAX_VALUE}, then the result is
	 * equal to 2<sup>971</sup>.
	 * </ul>
	 *
	 * @param d the floating-point value whose ulp is to be returned
	 * @return the size of an ulp of the argument
	 * @author Joseph D. Darcy
	 * @since 1.5
	 */
	public static double ulp(double d) {
		return java.lang.Math.ulp(d);
	}

	/**
	 * Returns the size of an ulp of the argument. An ulp, unit in the last place,
	 * of a {@code float} value is the positive distance between this floating-point
	 * value and the {@code
	 * float} value next larger in magnitude. Note that for non-NaN <i>x</i>,
	 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, then the result is NaN.
	 * <li>If the argument is positive or negative infinity, then the result is
	 * positive infinity.
	 * <li>If the argument is positive or negative zero, then the result is
	 * {@code Float.MIN_VALUE}.
	 * <li>If the argument is &plusmn;{@code Float.MAX_VALUE}, then the result is
	 * equal to 2<sup>104</sup>.
	 * </ul>
	 *
	 * @param f the floating-point value whose ulp is to be returned
	 * @return the size of an ulp of the argument
	 * @author Joseph D. Darcy
	 * @since 1.5
	 */
	public static float ulp(float f) {
		return java.lang.Math.ulp(f);
	}

	/**
	 * Returns the signum function of the argument; zero if the argument is zero,
	 * 1.0 if the argument is greater than zero, -1.0 if the argument is less than
	 * zero.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, then the result is NaN.
	 * <li>If the argument is positive zero or negative zero, then the result is the
	 * same as the argument.
	 * </ul>
	 *
	 * @param d the floating-point value whose signum is to be returned
	 * @return the signum function of the argument
	 * @author Joseph D. Darcy
	 * @since 1.5
	 */
	public static double signum(double d) {
		return (d == 0.0 || Double.isNaN(d)) ? d : copySign(1.0, d);
	}

	/**
	 * Returns the signum function of the argument; zero if the argument is zero,
	 * 1.0f if the argument is greater than zero, -1.0f if the argument is less than
	 * zero.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, then the result is NaN.
	 * <li>If the argument is positive zero or negative zero, then the result is the
	 * same as the argument.
	 * </ul>
	 *
	 * @param f the floating-point value whose signum is to be returned
	 * @return the signum function of the argument
	 * @author Joseph D. Darcy
	 * @since 1.5
	 */
	public static float signum(float f) {
		return (f == 0.0f || Float.isNaN(f)) ? f : copySign(1.0f, f);
	}

	/**
	 * Returns the hyperbolic sine of a {@code double} value. The hyperbolic sine of
	 * <i>x</i> is defined to be (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/2
	 * where <i>e</i> is {@linkplain Math#E Euler's number}.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 *
	 * <li>If the argument is NaN, then the result is NaN.
	 *
	 * <li>If the argument is infinite, then the result is an infinity with the same
	 * sign as the argument.
	 *
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 2.5 ulps of the exact result.
	 *
	 * @param x The number whose hyperbolic sine is to be returned.
	 * @return The hyperbolic sine of {@code x}.
	 * @since 1.5
	 */
	public static double sinh(double x) {
		return java.lang.Math.sinh(x);
	}

	/**
	 * Returns the hyperbolic cosine of a {@code double} value. The hyperbolic
	 * cosine of <i>x</i> is defined to be
	 * (<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>)/2 where <i>e</i> is
	 * {@linkplain Math#E Euler's number}.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 *
	 * <li>If the argument is NaN, then the result is NaN.
	 *
	 * <li>If the argument is infinite, then the result is positive infinity.
	 *
	 * <li>If the argument is zero, then the result is {@code 1.0}.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 2.5 ulps of the exact result.
	 *
	 * @param x The number whose hyperbolic cosine is to be returned.
	 * @return The hyperbolic cosine of {@code x}.
	 * @since 1.5
	 */
	public static double cosh(double x) {
		return java.lang.Math.cosh(x);
	}

	/**
	 * Returns the hyperbolic tangent of a {@code double} value. The hyperbolic
	 * tangent of <i>x</i> is defined to be
	 * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>),
	 * in other words, {@linkplain Math#sinh sinh(<i>x</i>)}/{@linkplain Math#cosh
	 * cosh(<i>x</i>)}. Note that the absolute value of the exact tanh is always
	 * less than 1.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 *
	 * <li>If the argument is NaN, then the result is NaN.
	 *
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 *
	 * <li>If the argument is positive infinity, then the result is {@code +1.0}.
	 *
	 * <li>If the argument is negative infinity, then the result is {@code -1.0}.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 2.5 ulps of the exact result. The result
	 * of {@code tanh} for any finite input must have an absolute value less than or
	 * equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp
	 * of the limit value of &plusmn;1, correctly signed &plusmn;{@code 1.0} should
	 * be returned.
	 *
	 * @param x The number whose hyperbolic tangent is to be returned.
	 * @return The hyperbolic tangent of {@code x}.
	 * @since 1.5
	 */
	public static double tanh(double x) {
		return java.lang.Math.tanh(x);
	}

	/**
	 * Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>) without
	 * intermediate overflow or underflow.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 *
	 * <li>If either argument is infinite, then the result is positive infinity.
	 *
	 * <li>If either argument is NaN and neither argument is infinite, then the
	 * result is NaN.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. If one
	 * parameter is held constant, the results must be semi-monotonic in the other
	 * parameter.
	 *
	 * @param x a value
	 * @param y a value
	 * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>) without
	 *         intermediate overflow or underflow
	 * @since 1.5
	 */
	public static double hypot(double x, double y) {
		return java.lang.Math.hypot(x, y);
	}

	/**
	 * Returns <i>e</i><sup>x</sup>&nbsp;-1. Note that for values of <i>x</i> near
	 * 0, the exact sum of {@code expm1(x)}&nbsp;+&nbsp;1 is much closer to the true
	 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is NaN.
	 *
	 * <li>If the argument is positive infinity, then the result is positive
	 * infinity.
	 *
	 * <li>If the argument is negative infinity, then the result is -1.0.
	 *
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic. The result of {@code expm1} for any finite input must be
	 * greater than or equal to {@code -1.0}. Note that once the exact result of
	 * <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1 is within 1/2 ulp of the limit
	 * value -1, {@code -1.0} should be returned.
	 *
	 * @param x the exponent to raise <i>e</i> to in the computation of
	 *          <i>e</i><sup>{@code x}</sup>&nbsp;-1.
	 * @return the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
	 * @since 1.5
	 */
	public static double expm1(double x) {
		return java.lang.Math.expm1(x);
	}

	/**
	 * Returns the natural logarithm of the sum of the argument and 1. Note that for
	 * small values {@code x}, the result of {@code log1p(x)} is much closer to the
	 * true result of ln(1 + {@code x}) than the floating-point evaluation of
	 * {@code log(1.0+x)}.
	 *
	 * <p>
	 * Special cases:
	 *
	 * <ul>
	 *
	 * <li>If the argument is NaN or less than -1, then the result is NaN.
	 *
	 * <li>If the argument is positive infinity, then the result is positive
	 * infinity.
	 *
	 * <li>If the argument is negative one, then the result is negative infinity.
	 *
	 * <li>If the argument is zero, then the result is a zero with the same sign as
	 * the argument.
	 *
	 * </ul>
	 *
	 * <p>
	 * The computed result must be within 1 ulp of the exact result. Results must be
	 * semi-monotonic.
	 *
	 * @param x a value
	 * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural log of
	 *         {@code x}&nbsp;+&nbsp;1
	 * @since 1.5
	 */
	public static double log1p(double x) {
		return java.lang.Math.log1p(x);
	}

	/**
	 * Returns the first floating-point argument with the sign of the second
	 * floating-point argument. Note that unlike the
	 * {@link java.lang.Math#copySign(double, double) java.lang.Math.copySign}
	 * method, this method does not require NaN {@code sign} arguments to be treated
	 * as positive values; implementations are permitted to treat some NaN arguments
	 * as positive and other NaN arguments as negative to allow greater performance.
	 *
	 * @param magnitude the parameter providing the magnitude of the result
	 * @param sign      the parameter providing the sign of the result
	 * @return a value with the magnitude of {@code magnitude} and the sign of
	 *         {@code sign}.
	 * @since 1.6
	 */
	public static double copySign(double magnitude, double sign) {
		return java.lang.Math.copySign(magnitude, sign);
	}

	/**
	 * Returns the first floating-point argument with the sign of the second
	 * floating-point argument. Note that unlike the
	 * {@link java.lang.Math#copySign(float, float) java.lang.Math.copySign} method,
	 * this method does not require NaN {@code sign} arguments to be treated as
	 * positive values; implementations are permitted to treat some NaN arguments as
	 * positive and other NaN arguments as negative to allow greater performance.
	 *
	 * @param magnitude the parameter providing the magnitude of the result
	 * @param sign      the parameter providing the sign of the result
	 * @return a value with the magnitude of {@code magnitude} and the sign of
	 *         {@code sign}.
	 * @since 1.6
	 */
	public static float copySign(float magnitude, float sign) {
		return java.lang.Math.copySign(magnitude, sign);
	}

	/**
	 * Returns the unbiased exponent used in the representation of a {@code float}.
	 * Special cases:
	 *
	 * <ul>
	 * <li>If the argument is NaN or infinite, then the result is
	 * {@link Float#MAX_EXPONENT} + 1.
	 * <li>If the argument is zero or subnormal, then the result is
	 * {@link Float#MIN_EXPONENT} -1.
	 * </ul>
	 * 
	 * @param f a {@code float} value
	 * @return the unbiased exponent of the argument
	 * @since 1.6
	 */
	public static int getExponent(float f) {
		/*
		 * Bitwise convert f to integer, mask out exponent bits, shift to the right and
		 * then subtract out float's bias adjust to get true exponent value
		 */
		return java.lang.Math.getExponent(f);
	}

	/**
	 * Returns the unbiased exponent used in the representation of a {@code double}.
	 * Special cases:
	 *
	 * <ul>
	 * <li>If the argument is NaN or infinite, then the result is
	 * {@link Double#MAX_EXPONENT} + 1.
	 * <li>If the argument is zero or subnormal, then the result is
	 * {@link Double#MIN_EXPONENT} -1.
	 * </ul>
	 * 
	 * @param d a {@code double} value
	 * @return the unbiased exponent of the argument
	 * @since 1.6
	 */
	public static int getExponent(double d) {
		return java.lang.Math.getExponent(d);
	}

	/**
	 * Returns the floating-point number adjacent to the first argument in the
	 * direction of the second argument. If both arguments compare as equal the
	 * second argument is returned.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If either argument is a NaN, then NaN is returned.
	 *
	 * <li>If both arguments are signed zeros, {@code direction} is returned
	 * unchanged (as implied by the requirement of returning the second argument if
	 * the arguments compare as equal).
	 *
	 * <li>If {@code start} is &plusmn;{@link Double#MIN_VALUE} and
	 * {@code direction} has a value such that the result should have a smaller
	 * magnitude, then a zero with the same sign as {@code start} is returned.
	 *
	 * <li>If {@code start} is infinite and {@code direction} has a value such that
	 * the result should have a smaller magnitude, {@link Double#MAX_VALUE} with the
	 * same sign as {@code start} is returned.
	 *
	 * <li>If {@code start} is equal to &plusmn; {@link Double#MAX_VALUE} and
	 * {@code direction} has a value such that the result should have a larger
	 * magnitude, an infinity with same sign as {@code start} is returned.
	 * </ul>
	 *
	 * @param start     starting floating-point value
	 * @param direction value indicating which of {@code start}'s neighbors or
	 *                  {@code start} should be returned
	 * @return The floating-point number adjacent to {@code start} in the direction
	 *         of {@code direction}.
	 * @since 1.6
	 */
	public static double nextAfter(double start, double direction) {
		return java.lang.Math.nextAfter(start, direction);
	}

	/**
	 * Returns the floating-point number adjacent to the first argument in the
	 * direction of the second argument. If both arguments compare as equal a value
	 * equivalent to the second argument is returned.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If either argument is a NaN, then NaN is returned.
	 *
	 * <li>If both arguments are signed zeros, a value equivalent to
	 * {@code direction} is returned.
	 *
	 * <li>If {@code start} is &plusmn;{@link Float#MIN_VALUE} and {@code direction}
	 * has a value such that the result should have a smaller magnitude, then a zero
	 * with the same sign as {@code start} is returned.
	 *
	 * <li>If {@code start} is infinite and {@code direction} has a value such that
	 * the result should have a smaller magnitude, {@link Float#MAX_VALUE} with the
	 * same sign as {@code start} is returned.
	 *
	 * <li>If {@code start} is equal to &plusmn; {@link Float#MAX_VALUE} and
	 * {@code direction} has a value such that the result should have a larger
	 * magnitude, an infinity with same sign as {@code start} is returned.
	 * </ul>
	 *
	 * @param start     starting floating-point value
	 * @param direction value indicating which of {@code start}'s neighbors or
	 *                  {@code start} should be returned
	 * @return The floating-point number adjacent to {@code start} in the direction
	 *         of {@code direction}.
	 * @since 1.6
	 */
	public static float nextAfter(float start, double direction) {
		return java.lang.Math.nextAfter(start, direction);
	}

	/**
	 * Returns the floating-point value adjacent to {@code d} in the direction of
	 * positive infinity. This method is semantically equivalent to
	 * {@code nextAfter(d,
	 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} implementation may run
	 * faster than its equivalent {@code nextAfter} call.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is NaN.
	 *
	 * <li>If the argument is positive infinity, the result is positive infinity.
	 *
	 * <li>If the argument is zero, the result is {@link Double#MIN_VALUE}
	 *
	 * </ul>
	 *
	 * @param d starting floating-point value
	 * @return The adjacent floating-point value closer to positive infinity.
	 * @since 1.6
	 */
	public static double nextUp(double d) {
		if (Double.isNaN(d) || d == Double.POSITIVE_INFINITY)
			return d;
		else {
			d += 0.0d;
			return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + ((d >= 0.0d) ? +1L : -1L));
		}
	}

	/**
	 * Returns the floating-point value adjacent to {@code f} in the direction of
	 * positive infinity. This method is semantically equivalent to
	 * {@code nextAfter(f,
	 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} implementation may run
	 * faster than its equivalent {@code nextAfter} call.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is NaN.
	 *
	 * <li>If the argument is positive infinity, the result is positive infinity.
	 *
	 * <li>If the argument is zero, the result is {@link Float#MIN_VALUE}
	 *
	 * </ul>
	 *
	 * @param f starting floating-point value
	 * @return The adjacent floating-point value closer to positive infinity.
	 * @since 1.6
	 */
	public static float nextUp(float f) {
		return java.lang.Math.nextUp(f);
	}

	/**
	 * Returns the floating-point value adjacent to {@code d} in the direction of
	 * negative infinity. This method is semantically equivalent to
	 * {@code nextAfter(d,
	 * Double.NEGATIVE_INFINITY)}; however, a {@code nextDown} implementation may
	 * run faster than its equivalent {@code nextAfter} call.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is NaN.
	 *
	 * <li>If the argument is negative infinity, the result is negative infinity.
	 *
	 * <li>If the argument is zero, the result is {@code -Double.MIN_VALUE}
	 *
	 * </ul>
	 *
	 * @param d starting floating-point value
	 * @return The adjacent floating-point value closer to negative infinity.
	 * @since 1.8
	 */
	public static double nextDown(double d) {
		if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
			return d;
		else {
			if (d == 0.0)
				return -Double.MIN_VALUE;
			else
				return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + ((d > 0.0d) ? -1L : +1L));
		}
	}

	/**
	 * Returns the floating-point value adjacent to {@code f} in the direction of
	 * negative infinity. This method is semantically equivalent to
	 * {@code nextAfter(f,
	 * Float.NEGATIVE_INFINITY)}; however, a {@code nextDown} implementation may run
	 * faster than its equivalent {@code nextAfter} call.
	 *
	 * <p>
	 * Special Cases:
	 * <ul>
	 * <li>If the argument is NaN, the result is NaN.
	 *
	 * <li>If the argument is negative infinity, the result is negative infinity.
	 *
	 * <li>If the argument is zero, the result is {@code -Float.MIN_VALUE}
	 *
	 * </ul>
	 *
	 * @param f starting floating-point value
	 * @return The adjacent floating-point value closer to negative infinity.
	 * @since 1.8
	 */
	public static float nextDown(float f) {
		if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
			return f;
		else {
			if (f == 0.0f)
				return -Float.MIN_VALUE;
			else
				return Float.intBitsToFloat(Float.floatToRawIntBits(f) + ((f > 0.0f) ? -1 : +1));
		}
	}

	/**
	 * Returns {@code d} &times; 2<sup>{@code scaleFactor}</sup> rounded as if
	 * performed by a single correctly rounded floating-point multiply to a member
	 * of the double value set. See the Java Language Specification for a discussion
	 * of floating-point value sets. If the exponent of the result is between
	 * {@link Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the answer is
	 * calculated exactly. If the exponent of the result would be larger than
	 * {@code Double.MAX_EXPONENT}, an infinity is returned. Note that if the result
	 * is subnormal, precision may be lost; that is, when {@code scalb(x, n)} is
	 * subnormal, {@code scalb(scalb(x, n), -n)} may not equal <i>x</i>. When the
	 * result is non-NaN, the result has the same sign as {@code d}.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If the first argument is NaN, NaN is returned.
	 * <li>If the first argument is infinite, then an infinity of the same sign is
	 * returned.
	 * <li>If the first argument is zero, then a zero of the same sign is returned.
	 * </ul>
	 *
	 * @param d           number to be scaled by a power of two.
	 * @param scaleFactor power of 2 used to scale {@code d}
	 * @return {@code d} &times; 2<sup>{@code scaleFactor}</sup>
	 * @since 1.6
	 */
	public static double scalb(double d, int scaleFactor) {
		return java.lang.Math.scalb(d, scaleFactor);
	}

	/**
	 * Returns {@code f} &times; 2<sup>{@code scaleFactor}</sup> rounded as if
	 * performed by a single correctly rounded floating-point multiply to a member
	 * of the float value set. See the Java Language Specification for a discussion
	 * of floating-point value sets. If the exponent of the result is between
	 * {@link Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the answer is
	 * calculated exactly. If the exponent of the result would be larger than
	 * {@code Float.MAX_EXPONENT}, an infinity is returned. Note that if the result
	 * is subnormal, precision may be lost; that is, when {@code scalb(x, n)} is
	 * subnormal, {@code scalb(scalb(x, n), -n)} may not equal <i>x</i>. When the
	 * result is non-NaN, the result has the same sign as {@code f}.
	 *
	 * <p>
	 * Special cases:
	 * <ul>
	 * <li>If the first argument is NaN, NaN is returned.
	 * <li>If the first argument is infinite, then an infinity of the same sign is
	 * returned.
	 * <li>If the first argument is zero, then a zero of the same sign is returned.
	 * </ul>
	 *
	 * @param f           number to be scaled by a power of two.
	 * @param scaleFactor power of 2 used to scale {@code f}
	 * @return {@code f} &times; 2<sup>{@code scaleFactor}</sup>
	 * @since 1.6
	 */
	public static float scalb(float f, int scaleFactor) {
		return java.lang.Math.scalb(f, scaleFactor);
	}
}
